[CvGmt News] Seminari Calcolo delle Variazioni
alberti at mail.dm.unipi.it
alberti at mail.dm.unipi.it
Mon Feb 14 15:10:16 CET 2005
Seminari di calcolo delle variazioni
when: Wednesday, February 16, at 6 pm
where: Departiment of Mathematics, Sala delle Riunioni
speaker: Antonio Siconolfi (Roma I)
title: Aubry set and applications
abstract: For a given Hamiltonian H(x,p) continuous and quasiconvex in
the second argument, defined in RN *RN or on the cotangent bundle of a
compact boundaryless manifold, we consider the equation H = c with c
critical value, i.e. for which the equation admits locally
Lipschitz-continuous a.e. subsolutions, but not strict subsolutions.
We show that there is a subset of the state variable space, called
Aubry set and denoted by \A, where the obstruction to the existence
of such subsolution is concentrated. We give a metric characterization
of \A, and we discuss its main properties. They are applied to a
projection problem in a Banach space, to the study of the large-time
behavior of subsolutions to a time-dependent Hamilton-Jacobi equation,
and to construct a Lyapunov function for a perturbed dynamics, under
suitable stability assumptions.
Reference: http://www.dm.unipi.it/~alberti/files/altrepagine/SeminarioCVGMT/home.html#future
You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20050216/
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